Interior-point algorithm for linear programming based on a new descent direction

Zaoui Billel, Benterki Djamel, Kraria Aicha, Raouache Hadjer
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Abstract

We present a full-Newton step feasible interior-point algorithm for linear optimization based on a new search direction. We apply a vector-valued function generated by a univariate function on a new type of transformation on the centering equations of the system which characterizes the central path. For this, we consider a new function ψ(t)=t 7/4 . Furthermore, we show that the algorithm finds the epsilon-optimal solution of the underlying problem in polynomial time. Finally, a comparative numerical study is reported in order to analyze the efficiency of the proposed algorithm.
基于新下降方向的内点线性规划算法
提出了一种基于新搜索方向的全牛顿阶跃可行内点线性优化算法。我们将一个由单变量函数生成的向量值函数应用于表征中心路径的系统定心方程上的一种新型变换。为此,我们考虑一个新的函数ψ(t)=t 7/4。此外,我们证明了该算法在多项式时间内找到了潜在问题的最优解。最后,通过数值对比研究,分析了该算法的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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